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<front>
<journal-meta>
<journal-id journal-id-type="publisher">EGUsphere</journal-id>
<journal-title-group>
<journal-title>EGUsphere</journal-title>
<abbrev-journal-title abbrev-type="publisher">EGUsphere</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">EGUsphere</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub"></issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/egusphere-2026-5146</article-id>
<title-group>
<article-title>Integration of physics-informed deep learning with a distributed hydrological model (PIDL-DHM): A hybrid model for runoff simulation</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wang</surname>
<given-names>Junping</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Xue</surname>
<given-names>Baolin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wang</surname>
<given-names>Guoqiang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Innovation Research Center of Satellite Application (IRCSA), Faculty of Geographical Science, Beijing Normal University, Beijing, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>National Institute of Natural Hazards, Ministry of Emergency Management of the People’s Republic of China, Beijing, 100085, China</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Autonomous Region Collaborative Innovation Center for Integrated Management of Water Resources and Water Environment in the Inner Mongolia  Reaches of the Yellow River, Hohhot 010018, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>15</day>
<month>09</month>
<year>2026</year>
</pub-date>
<volume>2026</volume>
<fpage>1</fpage>
<lpage>62</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2026 Junping Wang et al.</copyright-statement>
<copyright-year>2026</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-5146/">This article is available from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-5146/</self-uri>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-5146/egusphere-2026-5146.pdf">The full text article is available as a PDF file from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-5146/egusphere-2026-5146.pdf</self-uri>
<abstract>
<p>Climate change and vegetation restoration have altered hydrological processes, but quantifying vegetation-runoff interactions remains challenging due to complex feedback and data scarcity. We developed a physics-informed deep learning hybrid model that couples process-based hydrology with deep learning to improve runoff prediction in vegetation-altered basins. The model explicitly represents transpiration, interception, snow dynamics, dual runoff generation, water-balance constraints, and distributed spatial heterogeneity. Evaluations in three Chinese basins spanning hydroclimatic and vegetation gradients show that the hybrid models outperform pure deep learning, with the strongest improvements in semi-arid and vegetation-transition basins. Correlation coefficients exceeded 0.8 at monthly/annual scales and 0.75 at daily scales in the most responsive basins. Compared with GR4J, the added complexity is most beneficial in heterogeneous semi-arid and ungauged sub-basins. These results demonstrate that physical constraints improve extrapolation reliability and support hybrid models for sustainable basin management under climate change.</p>
</abstract>
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<funding-group>
<award-group id="gs1">
<funding-source>National Science Fund for Distinguished Young Scholars</funding-source>
<award-id>52125901</award-id>
<award-id>National Natural Science Foundation of China</award-id>
<award-id>52379002</award-id>
</award-group>
</funding-group>
</article-meta>
</front>
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